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A nonlocal graph-PDE and higher-order geometric integration for image labeling

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This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in \textit{J.~Math.~Imaging \& Vision} 58(2), 2017. Due to this parameterization,...

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Bibliographische Detailangaben
Hauptverfasser: Sitenko, Dmitrij (VerfasserIn) , Boll, Bastian (VerfasserIn) , Schnörr, Christoph (VerfasserIn)
Dokumenttyp: Article (Journal) Kapitel/Artikel
Sprache:Englisch
Veröffentlicht: 4 Oct 2022
Ausgabe:Version v2
In: Arxiv
Year: 2022, Pages: 1-60
DOI:10.48550/arXiv.2205.03991
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2205.03991
Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2205.03991
Volltext
Verfasserangaben:Dmitrij Sitenko, Bastian Boll, Christoph Schnörr

MARC

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520 |a This paper introduces a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in \textit{J.~Math.~Imaging \& Vision} 58(2), 2017. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with respect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for integrating the assignment flow is equivalent to solving the G-PDE by an established DC programming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments. 
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